Applying a fundamental mathematical insight to the problem of turbulence.
Turbulence surrounds us. It is in the plume of breath rising above us as we speak; the flow of gas through a pipeline; blood through an artery; steam powering a generator; clouds becoming storms; and air lifting an airplane wing. But despite this ubiquity, our understanding of turbulent fluid mechanics is incomplete. Even in the most sophisticated computer models, turbulence is a special case: there is an intricate energy exchange that occurs between fluid fluctuations at all length scales, including those too small to simulate. Scientists and engineers typically compensate by building physical models, and then tinkering with their computer simulations until they match. “But there is minimal predictive power in that, and engineering progress has largely been incremental,” says Justin Beroz, a double PhD at MIT in the departments of physics and mechanical engineering. “A full theoretical understanding of turbulence would be transformational. We could finally find out how much better our engineered systems can really be.”
ReynKo Inc., founded by Beroz, uses a breakthrough approach to transform existing methods of modeling and controlling turbulence. Specifically, Beroz has developed a mathematical framework and solution to the Navier-Stokes equations, one of the most important sets of equations in physics, which describe the motion of fluids. Rather than relying on semi-empirical approximations, Beroz’s work has defined an exact fundamental theory for the dynamics of turbulent flows. “Plainly speaking, this brings unprecedented predictive power,” says Beroz. ReynKo’s new approach to modeling turbulence can be incorporated into existing computational fluid dynamics software, which is a crucial tool in the engineering of everything, from jet engines to medical devices to weather forecasts. As well, ReynKo’s fundamental insights will be applied to the design and fabrication of innovative turbulence suppression technologies.
Beroz came to the problem of turbulence from his early studies as a mechanical engineer. His abiding interest was invention, but, feeling limited by the tools at hand, he switched to MIT’s physics department to engage more directly with the field’s most basic rules. Turbulence was an important—and unresolved—question. Its mathematical understanding depended on the equations developed by Claude-Louis Navier and George Gabriel Stokes in the 19th century, which are famously difficult to solve. This is primarily due to the presence of a nonlinear term in the equations, which plays a crucial role in turbulent dynamics, but has resisted efforts to be manipulated in a fruitful way.
Beroz approached this underlying mathematical challenge from a new starting point. Rather than rely on what is known as the Reynolds decomposition to model turbulence, which uses the relationship between the mean and fluctuating parts of a turbulent flow, Beroz hypothesized an alternative decomposition that opened a novel pathway for formulating the math. With sustained attention, this ultimately yielded a complete general mathematical solution of Navier-Stokes for turbulent flows. When compared against the detailed work of experimentalists, the new mathematical model and existing empirical data agreed. The implications for pipe flow were particularly striking. “It turns out that there's one special wavelength of disturbance in a pipe that's actually responsible for the transition from laminar to turbulent flow,” Beroz explains. “And it's exactly equal to two pipe diameters.” With the assistance of John Bush and Steven Johnson, both in the department of mathematics at MIT, Beroz is working to publish these results.
ReynKo—named after Osborne Reynolds and Andrey Kolmogorov, two pioneers in the scientific understanding of turbulence—is applying its breakthrough understanding to practical challenges. Existing commercial computational fluid dynamics simulations rely on a range of modular plug-ins to describe turbulence—inexact approximations that can easily be replaced by ReynKo’s precise mathematical solutions. This increased predictive power can capture more of the design process in simulation, speeding the development of new methods to effectively control and suppress turbulence. This in turn brings the potential to revolutionize the engineering of existing equipment and methods across a vast array of industries: water networks, HVAC systems, chemical processing, hydroelectric power, oil and gas extraction and transport, aerospace, weather and climate prediction, and medicine.
“Ambitious as is the claim, it appears my mathematical theory has solved the longstanding ‘turbulence problem,’” says Beroz. “And it is thrilling to consider the new solutions for fluid engineering we will be able to unlock.”